194 research outputs found
Differentiating the absolutely continuous invariant measure of an interval map f with respect to f
Let the map have a.c.i.m. (absolutely continuous
-invariant measure with respect to Lebesgue). Let be the change
of corresponding to a perturbation of .
Formally we have, for differentiable , but this
expression does not converge in general. For real-analytic and Markovian in
the sense of covering times, and assuming an {\it analytic
expanding} condition, we show that
is meromorphic in , and has no pole at
. We can thus formally write .Comment: 10 pages, plain Te
Entropy production in quantum spin systems
We consider a quantum spin system consisting of a finite subsystem connected
to infinite reservoirs at different temperatures. In this setup we define
nonequilibrium steady states and prove that the rate of entropy production in
such states is nonnegative.Comment: In honor of J.L. Lebowit
How should one define entropy production for nonequilibrium quantum spin systems?
This paper discusses entropy production in nonequilibrium steady states for
infinite quantum spin systems. Rigorous results have been obtained recently in
this area, but a physical discussion shows that some questions of principle
remain to be clarified.Comment: 8 page
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